Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V _D , where V _D is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V _D , the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishing solute drag energy, i.e. partitionless and “dragless” solidification.     

Diffusionless crystal growth in a eutectic system during rapid solidification

Experiments on nonequilibrium rapid eutectic growth are surveyed. The applicability limits of the modern theoretical models describing rapid solidification of binary systems are assessed. A problem of rapid eutectic growth when the local equilibrium is violated in the solute diffusion field (in the bulk liquid and at the solid-liquid interface) is formulated. An analytical solution to the problem of rapid lamellar eutectic growth under local nonequilibrium conditions in the solute diffusion field is found. It is shown that the diffusion-limited growth of a eutectic pattern ceases as soon as a chemically homogeneous crystalline phase begins to grow when the critical point V=V _D is achieved (V is the solid-liquid interface velocity and V _D is the solute diffusion speed in the bulk liquid). At V ≥ V _D, eutectic decomposition is suppressed and the nascent homogeneous crystalline phase has the initial (nominal) chemical composition of the binary system.     

Solidification microstructure selection of the peritectic Nd-Fe-B alloys

Bridgman directional solidification and laser remelting experiments were carried out on Nd_11.76Fe_82.36B_5.88 and Nd_13.5Fe_79.75B_6.75 alloys. Microstructure evolutions along with solidification parameters (temperature gradient G, growth velocity V and initial alloy composition C ₀) were investigated. A solidification microstructure selection map was established, based on the consideration of solidification characteristics of peritectic T₁ phase. In Bridgman directional solidification experiments, with the increasing growth velocities, the morphology of T₁ phase changed from plane front or faceted plane front to dendrites. In laser remelting experiments, a transition from primary γ-Fe dendrites to T₁ dendrites was found. Theoretical predictions are in good agreement with experimental results. Supported by the National Natural Science Foundation of China (Grant No. 50395100)     

Theoretical analysis on the limitations of the open-circuit voltage of a hydrogenated amorphous silicon p-i-n solar cell

We have made theoretical studies on the limitation of the open-circuit voltageV _oc of a hydrogenated amorphous silicon (a-Si:H) p-i-n type solar cell. The effects of the tail states in the a-Si:H i layer and of the interface recombination are discussed in detail. The opencircuit voltage increases when the distribution of the tail states is sharp and/or the capture cross sections of these states are small. This is because the recombination rate of photogenerated carriers and/or the density of space charge due to trapped carriers in these states become low in these conditions. These effects of the tail states on the value ofV _oc become pronounced when the built-in potential of the p-i-n junction is high. The decrease in the effective recombination velocity of carriers at the p/i and n/i interfaces results in an increase ofV _oc. This increase becomes remarkable when the effects of the tail states on the value ofV _oc are small. Both the sharp distribution of tail states and the small value of the interface recombination velocity are necessary to increase considerably the value ofV _oc. We show the conditions of the material parameters necessary to obtain an open-circuit voltage of 1.0 V.     

三种变速条件下共晶生长的多相场法模拟

利用多相场模型模拟了共晶合金CBr₄-C₂Cl₆定向凝固变速生长过程，研究了阶跃变速、线性变速以及震荡变速三种变速条件下共晶片层间距的调整以及形态的变化.结果表明：在变速生长过程中，界面平均生长速率与平均过冷度随抽拉速率的变化均产生滞后效应；阶跃增速时，片层间距的调整通过突变分岔形式进行，而阶跃减速时，通过片层的逐步湮没与合并以及自身相的长大方式进行，两个过程表现出强烈的非对称性；线性增速过程，片层间距的调整通过逐步分岔进行，而线性减速过程 关键词： 多相场 共晶 变速生长 片层间距     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

三维多相场数值模拟共晶CBr4-C2Cl6合金在不同抽拉速度下的形态选择

利用KKSO多相场模型对定向凝固共晶CBr₄-C₂Cl₆合金的三维恒速及变速生长过程进行了研究,再现了不同抽拉速度下共晶形态演化及选择过程,建立了形态选择图,研究了变速过程的界面平均生长速度及界面平均过冷度的变化.结果表明,变速前后的形态选择与恒速下的形态选择一致;变速过程的形态演变、界面平均生长速度和界面平均过冷度的变化均产生滞后效应;界面平均生长速度和界面平均过冷度之间的关系与理论结果符合较好. 关键词： 多相场模型 共晶生长 抽拉速度     

Probability diffusion in non-Markhovian,non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule ofC _2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocityV. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V ²(t)V ²(0)>/<V ²(0)V ²(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.     

Magnetic field diffusion during a metal-insulator phase transition

An analysis is made of the diffusion of a static (slowly varying) magnetic field in a conductor in which a first-order phase transition to the insulating state takes place under the action of the Joule heating. An investigation is made of the case of subsonic propagation of the phase boundary. A (V_1−X Cr_X)₂O₃ solid solution is analyzed as a model substance. The application of this effect in pulsed high-current circuit breakers is discussed. Zh. Tekh. Fiz. 68, 43–48 (December 1998)     

Phase separation and rapid solidification of liquid Cu<Subscript>60</Subscript>Fe<Subscript>30</Subscript>Co<Subscript>10</Subscript> ternary peritectic alloy

The metastable liquid phase separation and rapid solidification of Cu₆₀Fe₃₀Co₁₀ ternary peritectic alloy were investigated by using the drop tube technique and the differential scanning calorimetry method. It was found that the critical temperature of metastable liquid phase separation in this alloy is 1623.5 K, and the two separated liquid phases solidify as Cu(Fe,Co) and Fe(Cu,Co) solid solutions, respectively. The undercooling and cooling rate of droplets processed in the drop tube increase with the decrease of their diameters. During the drop tube processing, the structural morphologies of undercooled droplets are strongly dependent on the cooling rate. With the increase of the cooling rate, Fe(Cu,Co) spheres are refined greatly and become uniformly dispersed in the Cu-rich matrix. The calculations of Marangoni migration velocity (V _M) and Stokes motion velocity (V _S) of Fe(Cu,Co) droplets indicated that Marangoni migration contributes more to the coarsening and congregation of the minor phase during free fall. At the same undercooling, the V _M/V _S ratio increases drastically as Fe(Cu,Co) droplet size decreases. On the other hand, a larger undercooling tends to increase the V _M/V _S value for Fe(Cu,Co) droplets with the same size. Supported by the National Natural Science Foundation of China (Grant Nos. 50121101 and 50395105) and the Scientific and Technological Creative Foundation of Youth in Northwestern Polytechnical University of China (Grant No. W016223)     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr     

The wettability and interfacial characterization between γ-TiAl alloy and ceramic reinforcements

The wettability and interfacial characterization of γ-TiAl alloy on TiC_0.78, TiN_0.87, and VNx substrates were studied using the Sessile Drop method at 1758 K. The equilibrium apparent contact angle of liquid γ-TiAl alloy are 8° on TiC_0.78 substrate, 22° on TiN_0.87, but deficient for VNx substrate because of the gradual appearance of solidification phenomena. The spreading mechanism of γ-TiAl/TiC_0.78 was ascribed to the product control model, which was determined by the new Ti₂AlC formed at the interface. The decreased apparent contact angle of γ-TiAl on TiN_0.87 substrate with the slow rate resulted from the combined effect of Ti adsorption at the interface and the decreased surface tension and viscosity of the liquid. The γ-TiAl/VNx system was a dissolution system. The effect of dissolution on apparent contact angle is reflected in the initial stage and progressed synchronously with the movement of the triple-phase line.     

Enhancement of measurement accuracy of X‐ray PIV in comparison with the micro‐PIV technique

The X‐ray PIV (particle image velocimetry) technique has been used as a non‐invasive measurement modality to investigate the haemodynamic features of blood flow. However, the extraction of two‐dimensional velocity field data from the three‐dimensional volumetric information contained in X‐ray images is technically unclear. In this study, a new two‐dimensional velocity field extraction technique is proposed to overcome technological limitations. To resolve the problem of finding a correction coefficient, the velocity field information obtained by X‐ray PIV and micro‐PIV techniques for disturbed flow in a concentric stenosis with 50% severity was quantitatively compared. Micro‐PIV experiments were conducted for single‐plane and summation images, which provide similar positional information of particles as X‐ray images. The correction coefficient was obtained by establishing the relationship between velocity data obtained from summation images (V_S) and centre‐plane images (V_C). The velocity differences between V_S and V_C along the vertical and horizontal directions were quantitatively analysed as a function of the geometric angle of the test model for applying the present two‐dimensional velocity field extraction technique to a conduit of arbitrary geometry. Finally, the two‐dimensional velocity field information at arbitrary positions could be successfully extracted from X‐ray images by using the correction coefficient and several velocity parameters derived from V_S.     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Hydromagnetic surface waves in a moving compressible plasma column

Summary The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when one of the fluids has a relative motion has been studied as a function of the compressibility factors ₁/V ₁, wheres ₁ andV ₁ are the acoustic and Alfvén wave speed in one of the media. Both slow and fast magnetosonic surface waves for each symmetric and asymmetric modes can exist. The nature and existence of these modes depend on the values ofs ₁/V ₁ and ϑ, the angle of wave propagation. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle ϑ. The authors of this paper have agreed to not receive the proofs for correction.     

Forward light reflection from a moving inhomogeneity

The reflection of monochromatic and quasi-monochromatic pulsed light incident on a moving inhomogeneity in the optical characteristics of a medium having plasma-type dispersion has been analyzed. The velocity V of the inhomogeneity, induced in the medium by an intense laser pulse, has been changed by varying its carrier frequency. It has been shown that the usual back-reflection mode, when the reflected radiation pulse moves in the direction opposite the direction of incident radiation, is implemented only if the velocity V is less than the critical value V _min, which depends on the carrier frequency of the incident radiation pulse. It has been found that reflected radiation moves in the same direction as the incident radiation in a certain range of the velocity V _min < V < V _max (forward reflection). In this case, the reflected radiation pulse begins to lag behind a fast-moving inhomogeneity. When V _max < V < c, where c is the speed of light in vacuum, the group velocity of the incident radiation pulse is less than the speed of inhomogeneity, and there is no reflection. Analytical treatment is supported by numerical simulation.     

Transport and dielectric properties of V2O5-MnO-TeO2 glasses

The frequency (1-10 kHz) and temperature (80-350 K) dependences of the ac conductivity and dielectric constant of the V₂O₅-MnO-TeO₂ system, containing two transition-metal ions, have been measured. The dc conductivity _dc measured in the high-temperature range (200-450 K) decreases with addition of the oxide MnO. This is considered to be due to the formation of bonds such as V--O--Mn and Mn--O--Mn in the glass. The conductivity arises mainly from polaron hopping between V^4+M and V⁵⁺ ions. It is found that a mechanism of adiabatic small-polaron hopping is the most appropriate conduction model for these glasses. This is in sharp contrast with the behaviour of the Mn-free V₂O₅-TeO₂ glass, in which non-adiabatic hopping takes place. High-temperature conductivity data satisfy Mott's small-polaron hopping model and also a model proposed by Schnakenberg in 1968. A power-law behaviour ( _ac = Aω^s , with s < 1) is well exhibited by the ac conductivity σ_ac data of these glasses. Analysis of dielectric data indicates a Debye-type relaxation behaviour with a distribution of relaxation times. The MnO-concentration-dependent σ_ac data follow an overlapping large-polaron tunnelling model over the entire range of temperatures studied. The estimated model parameters are reasonable and consistent with changes in composition.     

Numerical simulation on the operational characteristics of the pulsed inductive acceleration

To analyse the ionization and acceleration properties of an inductive plasma excited by a pulsed current flowing through the planar coil, the extended GLM formulations of the MHD (EGLM‐MHD) model, combined with the high‐temperature thermodynamic and transport model, is employed to simulate the characteristics of the flow. The two‐dimensional axisymmetric calculation captures the generation, growth, and acceleration of the current sheet, and the process is completed in the first half period. The sheet is mainly comprised of lower ionization level ions in the front and higher level ions at the back, and the density is one order higher than that of the residual plasma on the coil surface. As the abscissa value of the sheet is larger than the decoupling distance, a reversed flow emerges, generating a backward impulse, and the negative velocity can be more than 15 km/s at peak intensity B₀ = 0.5 T. In the second 1/4 period, the magnetic field and current density distribute non‐linearly on the surface and regularly in the sheet, caused by the reversing of the changing rate of the magnetic field and the particles' radial diffusion. The results at different intensities show that, for the same coil size, the time at which the maximum velocity V_max appears is advanced as the intensity increases, and V_max can be greater than 20 km/s above 0.5 T.     

Integral equation theory of the exchange potential,HOMO–LUMO properties,and sum rules for the exchange-correlation force

Recently, a formally exact integral equation for the exchange potential V _x(r) has been presented by the authors. In the admittedly simplistic limit in which Slater–Kohn–Sham and Hartree–Fock determinants become equal, this integral equation reduces to that given by Della Sala and Görling. Here, a proposal is made to relate, but now approximately, the formally exact equation for V _x(r) to HOMO–LUMO properties. The addition of a correlation contribution V _c(r) to V _x(r), the sum being the exchange-correlation potential V _xc(r), is finally considered, some exact properties and especially sum rules for the force ??V _xc/?r being the focus.